Interpreting global (stellar) kinematics of the disk, in terms of spirals

Background and Set-Up

Eilers and Hogg have created "global" stellar kinematic map of the Galactic disk, with 6D information on ~20.000 stars extending in RGC from 0 to 20 kpc. Between 6kpc and 13 kpc [TBC]

this map shows nice "spiraly" radial velocity pattern, that we should attribute to a "spiral perturbation". 

The question is what practical ways are to interpret these data in terms of (dynamical) spiral arm perturbation (its strength, pattern speed and morphology). 

These notes hare have emerged from conversations between C. Eilers, J-B Fouvry and H-W Rix in HD, and serve (among other things) to bring D. Hogg in the loop.

The observational information

This "map" is actually n(R,phi,z,vphi,vR,vz) == f(R,phi,z,vphi,vR,vz) x S(R,phi,z,vphi,vR,vz),

where S(R,phi,z,vphi,vR,vz) is the selection function.

The main issue with the selection function is that it separates into

 S(R,phi,z,vphi,vR,vz)=S(R,phi,z) x S(vphi,vR,vz), where S(R,phi,z) = very complex, and S(vphi,vR,vz)=const. The selection function can be writen as S (D | phi,theta)*S(phi)*S(theta), where

R=Ro-D*cos(l) cos(theta) and z=D*cos(theta); S(phi) and S(theta) are highly structured, S(D | ..) is (kind-of) smooth.

Rather than modelling the fill distribution function in action-angle space F(J,theta) [the "other theta"],

we se whether there is a sub-space, where the selection function is flat, taking advantage of S(vphi,vR,vz | D,phi,theta)=const.

The proposal here is to model the radial actions and radial angles; as their experimental selection effects may be benign.

Conceptual modelling approach:

We observed a distribution of stars in the disk, which is approximately axisymmetric, but has significant non-axisymmetries (see above). We would like to link that to a driving non-axisymmetric, time-dependent perturbation, focussing on the region >5kpc, as the pattern speeds are slow enough

that co-rotation (and hopefully other resonances) is 'far out'. [JBF stresses the importance of this!]

The problem of linking a time-dependent, non-axisymmetric potential to the resulting non-axisymmetric distribution function has been essentially (theoretically) solved (in the linear, and  non-self-consistent regime) by Monari & Famaey (2016), building on Section 5.1. in BT.

If one has solved the axisymmetric problem, Phi_0 and f_0, one can write for a small/linear deviation from it:

which then leads to the following select steps:

Propose a periodic (in phi) potential pewrturbation

then

spelled out in cylindrical coordinates

resulting in a (formally) closed solution with:

and other terms. Basically all this is spelled out in MF16.

Conceptually, the miracle is that the explicit time-dependence can be eliminated to a seeming steady-state solution in a co-rotating frame (Eq 15 --> 16 in MF16).

Implementation issues:

Here are some suggestions (to Christina) how to implement it:

-- go through the Monari&Famaey paper and re-write/simply it to the 2D case of a razor-thin disk;

    probably a good idea to wrapy your mind around the math.

-- let's choose a very simple Phi_1 perturbation functional form, to have something specific.

-- we need to get Phi_0 and F_0!  

    let's presume that for the moment we only consider F(J_R,theta_R), i.e. the radial action/angle (for the reasons above).

    How do we then get F0(J_R,theta_R) = F0(J_R)?

    One way would be to determine Phi_0 and F0(J_R) simultaneously through 'orbital roulette' (== most plausible angle distribution); this may be an intereting project in itself:

 Or, we just adopt Phi_0(R) from Eilers,Hogg,Rix,Ness2019, and fit for F0(J_R).

 Note that we need to take subsequently derivatives of F0(J_R) w.r.t. J_R; this means we need

 to take (and fit) an analytic form; presumably a pseudo-isothermal from Binney (see Trick, Bovy etc.. 2017).

Envisioned outcome:

-- decide whether there is a plausible geometry for Phi_1(R,phi,t) that matches the data above.

-- if so, ask what Phi_1 amplitude is implied and put it in astrophysical context (simulations etc..)

    

Exploring and testing the ddPayne_LAMOST_DR5 results

Exploring the low-mass main sequence

This is to explore basic stellar parameters returned by PddP_L_DR5 for low-mass, very cool MS stars:

Let's start with a basic plot: the background density is the distribution of stars from DR5 with SNR_Z>30 (geared towards red stars); and the isochrone is PARSEC (3Gyrs, solar)

That brings up the first question:

There are basically no objects in this cut of DR5 whose mass (from CMD alone) is < 0.25Msun.<0 .25="" div="" m_sun.="">

Are there no such objects that got targetted? (in which band does LAMOST target)?

Or did they not go through the pipeline?

Then let's look at the basic parameters, logg and Teff 

Obviously, and perhaps unsurprisingly, things don't look good below 0.4M_sun!

The main question here for me is:

a) @Maosheng: did you not determine logg and Teff by (Bayesian) isochrone fitting, and make this an input?

b) is this simply a reflection of the training?

Wide Binary Observing Proposal (twins and not-twins)

Starting point:

 I would like to spend some time at the MW  meeting talking and thinking
about a possible proposal for FEROS on the 2.2m (deadline end of the month);
the goal (for me) is to see whether there is a scientifically complelling case, and
whether anyone's interested in collaborating.
The science goal would be to exploit a set of wide binaries from Gaia
(derived by Kareem and Haijun) as a laboratory of what can work (or not)
in chemichal tagging; and learn about  the largest separation binaries while we are at it...

Parent sample, and its subsample:

The starting point is the following sample of wide (100AU-50,000AU) binaries,
selected as pairs of stars of the same proper motion and parallax (contaminant cleaned).

Parent wide-binary sample from Gaia, with the apparent magnitude difference shown as a function of physical separation. The most striking feature (but not the only feature if interest here) is the sequence of bins (identical magnitudes/masses). The slight asymmetry (around 0) in DeltaG arises from the definition of component 1 and 2; and is uninteresting.

Let's call the binaries, where the two components are within 0.2mag, twins.

Same sample as above, but shown here as a function of apparent magnitude. Only stars G<12 feros="" font="" lend="" m.="" spectroscopy="" straightforward="" themselves="" to="" with="">

• 

  Same sample as above, restricted to the binaries where both components are brighter than 12mag

Science questions:

Let's presume the members of the pairs are sibblings, stars born at the same time in the same place from the "same" material (and let's question and observationally probe this assumption in a minute).

• twin wide binaries may be the "easiest" case to check how identical photospheric abundances are among siblings; the fact that these sibblings are twins eliminates or reduces the spectral differences arising from Teff, or logg as a complication. Are these identical in spectral space? This can probably be asked in a data driven way. 
• Are there exceptions to "undistinguishably identical abundances"? Can we explain them?
• If there are non-identical abundances, does their incidence depend on separation?
• non-twin sibblings provides us with stars born at the same time from the same material, but with different masses.
• their abundance differences (on the MS) would inform us about atomic diffusion (heavy element settling)
• provide us with numerous empirical examples how spectra look like thatdiffere mostly because of logg,Teff; this is particularly important in the regime where spectral models  are problematic, such as Teff<3000k .="" aspects="" but:="" can="" li="" nbsp="" these="" two="" untangle="" we="">

The data at the same time would provide a means to check how clean that sample is, whether it contains any hiearchical triplets etc...

Observations:

At FEROS one gets full-coverage optical Echelle spectra 3600-9000A with S/N~50 AT G=12 (solar type star) in 10min, according to

 http://www.eso.org/observing/etc/bin/gen/form?INS.NAME=FEROS++INS.MODE=spectro

So, this makes spectroscopy of 100 pairs straightforward (50-80h), of 1000 pairs feasible; but that would need serious justification.

hot stars for SDSS-V (addendum 2)

Following up on the original post, I did the following variant:

The goal is to find massive stars, essentially by their two characteristics:
 they are luminous (abs(K)<-1, and they are hot, i.e. blue in unreddened colors.
The selection here is focussed on stars with some Gaia detection; even if the parallax
measurement is seemingly "marginal", it is powerful at ruling out all the low velocity stars.
The remaining challenge then is to separate luminous giant from luminous hot stars in the the presence of severe reddening. This can be done ad-hoc by devising self-dereddening colors, or (YST has done that with me) by taking BP,G,RP,J,H,K,W1 for stars with Apogee T_eff and training a neural net to predict T_eff in the presence of severe reddening; this seems to work beautifully, except that the training set is limited to 3500K<T_eff<8000K; this can be overcome.

Upshot of all of this: HWR's  naive view is that this works well (completeness and purity), as long as there is some Gaia information. Clean selection of massive stars that are H<12 or H<13, yet undetected in Gaia (say, G>19) remains a challenge, even conceptually.

Inspired by the hot-cool star separation (previous post, among absK<0),

I ran the query:

SELECT  g.*, tm.*, sqrt(g.phot_g_n_obs)/g.phot_g_mean_flux_over_error as variability
FROM gaiadr2.gaia_source AS g
INNER JOIN gaiadr1.tmass_best_neighbour AS xmatch
 ON g.source_id = xmatch.source_id
INNER JOIN gaiadr1.tmass_original_valid AS tm
 ON tm.tmass_oid = xmatch.tmass_oid
WHERE
tm.h_m < 12.
and
g.phot_g_mean_mag < 18.
and
( g.bp_rp < 1.  or  ( tm.j_m - tm.ks_m - 0.25*(g.phot_g_mean_mag - tm.ks_m) < 0.) )
and 
g.bp_rp < 2.
and
tm.j_m - tm.ks_m - 0.25*(g.phot_g_mean_mag - tm.ks_m) > -0.2
and
parallax < power(10.,(10.-tm.ks_m-1.)/5.)

which yielded:

I made a cut at bp_rp < 2, to cut out reddened variable sources.

Then I took the "massive stars regime"  at

then we get on sky for 40.000 objects:

those with 3sig parallaxes are:

Aside? Should I be worried that I don's see Orion?

Now let me just show what the plot looks like with the Teff estimates, derived from
BP,G,RP,J,H,K,W1 (trained to predict APOGEE Teff; courtesy Yuan-Sen Ting)

Here is a plot of NN-inferred (from colors) T_eff in the color-color plane:

The limiting (maximal) Teff is a consequence of the limited training set. The on-sky distibution of stars >6000K (16.000) of them at H<11.5 is here: (not bad?)

Addendum: November 2019

After the initial cuts, if one j_m - h_m - 0.13*(phot_g_mean_mag-ks_m) < 0.06, i.e.
makes another cut on on of these self-dereddened colors, one gets very "clean" samples.


In position space, they look like this:

and color coded by their G-K color (reddening), like this:

Detecting invisible companions to stars

The goal of the project is to develop strategies for how to detect "unseen massive" companions to regular stars, i.e. stars similar to the Sun (main sequence stars).

What do we mean by "unseen companions"?
Stars like the Sun can orbit (or be orbited) by a range of other astronomical objects:
-- by stars similar to them (binary stars)
-- by low-mass objects, foremost planet(s) or 'brown dwarfs'
-- by "stellar remnants", which could mean 'white dwarfs'(WD), 'neutron stars'(NS), or 'black
    holes'(BH); we presume that most stars that were massive enough to 'burn up their nuclear fuel'
    by now leave such remnants behind; as the mass of the progenitor stars increases,
    they leave behind WDs (M_init < 5M_sun), NS (5<M_init/M_sun<8), or BH (M_init >8M_sun)


In the present context, WD's are boring; NS are kind-of-boring, unless they have very masses (>2.xM_sun): the most massive NS constrain the neutron star equation of state. BH's left behind by stars are very exciting.

There are basically the reasons why BH's are exciting:
 -- they are so exotic, and we know so little about "stellar mass BHs"
 -- they are the ingredients in the most exciting gravitational wave events
 -- they tell us how stars die (see also below)

Why care about BH's in binary systems? So far, nobody has a good idea how to ever find a free-floating stellar-mass BH...

The only "stellar mass BHs" we know in the galaxy are ~15 'X-ray Binaries'. Those are systems where the orbit is so small that mass from the normal star gets torn off by tidal forces and streams onto the BH. In the course of this this material heats up very hot and shines in X-rays.
See: http://www-astro.physics.ox.ac.uk/~podsi/lec_c1_4_c.pdf
or
 [some very compact stellar evolution background at: http://www- astro.physics.ox.ac.uk/%7Epodsi/b3_stellar.pdf ]


We want to find many more BH's around normal stars, and those that orbit at greater distances. Why?
Having many more BH's tells us their "mass function"; as we know the mass function (i.e. mass probability distribution) of the progenitors, that provides information on "which star turns into what BH".
Why do we care about BH's orbiting more distant? If BH's form in Supernova explosions, then there is likely a recoil, as the explosion will not be perfectly symmetric. It is possible that only tightly bound stars stay in a binary after forming the BH. However, there are also theories that some stars form BHs simply by collapsing to a BH, without ever exploding as a supernova; then, there is of course no recoil.

for background, see e.g. http://www-astro.physics.ox.ac.uk/~podsi/lec_mm03.html
and this very relevant paper: https://arxiv.org/pdf/1710.04657.pdf
and
https://arxiv.org/pdf/1704.03455.pdf
[Note: these Gaia data will only be available in 2022.. we don't want to wait that long.]

How to find BH's orbiting other stars?
The most obvious approach would be to get spectra at many epochs, to get v_*(t). Taking spectra of millions of stars at many epochs is "expensive".

To search for them we should look for flux variations! E.g. the Gaia mission is mapping 10^9 stars, each >100 times.
And indeed, the tidal forces of an unseen companion "stretch" the stars, make it ellipsoidal. If we see it from the side, it has  larger projected area and is a bit brighter: this is called ellipsoidal distortion.

See: https://arxiv.org/abs/1106.2713 . Actually there are two more effects (as this paper shows); but the ellipsoidal distortions will be the strongest effect.

So, what to calculate and explore in this thesis?

Let's look at (and understand) the predicted amplitude A and the period P of the light modulation, as a function of the "underlying physical parameters": orbital separation, a, and the mass of the unseen object M_dark, for a, say, star of M_*=1M_sun; the amplitude also depends on the orbital inclination (if you look at a system "face on" --perpendicular to the orbital plane -- there is no variation).
[See the initial part of https://arxiv.org/abs/1106.2713 ]
I.e. derive A = f(M_dark,M_*,a,sin(i)), P= f(M_dark,M_*,a,sin(i)), and then ask
how M_dark depends on the observables (A,P,M_*), on sin(i) and on the quantity we want M_dark.

The first question is to answer: what physical properties can be determine from (an observed combination of) A and P alone? Are there unique signatures of BH companions (as opposed to
NS or WD)

What additional do we learn if we could determine the orbital inclination?

Then we will look at the (very model dependent) statistics of "how many BH's companions should show discernible signatures?" This is at the heart of the papers mentioned above:
https://arxiv.org/pdf/1710.04657.pdf
and
https://arxiv.org/pdf/1704.03455.pdf

So, how to start:
Work your way through the papers:
-- about populations:
https://arxiv.org/pdf/1710.04657.pdf
and
https://arxiv.org/pdf/1704.03455.pdf

-- about lightcurve variations due to unseen companions:
https://arxiv.org/abs/1106.2713

Variability in White Dwarfs (physics and Sample Selection)

Continuing on with my exploration of 'what variability in Gaia DR2 can do', I looked
at the Warwick GDR2 WD sample; variability == sqrt(phot_g_n_obs)/phot_g_mean_flux_over_error .
I restricted the following to G<18, as there the expected "shot-noise" contribution to this definition of variability is < 0.02mag.

If one looks at the WD sample, one sees that variability is very non-uniformly spread across the CMD, in good part as expected:

 or with larger dots

If I split the sample into a "non-variable" and variable" one, I get the following density maps.

Non-variable

and variable

I (as an absolute WD amateur) see three things:
-- variability is great to eliminate contaminants among faint (M=13) red (BP-RP~1.3) WDs
-- DAV (ZZ Ceti) stick out nicely, of course
-- are the hot variable WDs DBV stars??

Is any of that known (in this prettyness), is any of it interesting?

finding Cepheids through GDR2

Goal:

can one use GDR2 only to select a type I Cepheid sample for targetting; the basic idea is: 

a) they must be luminous absK<0, they must vary >0.3mag peak-to-peak, and they are blueish.

Dust extinction is the bain, of course.

How can one define 'photometric variability' in GDR2?

Via the photometric noise: sqrt(g.phot_g_n_obs)/g.phot_g_mean_flux_over_error

across the many epochs:

This depends on G-band magnitude, but for G<18 the "actual photon noise" is small:

There are many sources with excess noise, which at the bright end turns out to be most
commonly intrinsic variability:

What does Gaia DR2 "variability" quantify?

that looks good! For a sinusoid: 4*rms = peak-to-peak.

Query:

SELECT top 70000 * , sqrt(phot_g_n_obs)/phot_g_mean_flux_over_error as variability

FROM gaiadr2.gaia_source

WHERE

bp_rp < 2.

and

sqrt(phot_g_n_obs)/phot_g_mean_flux_over_error > 0.08

and

phot_g_mean_mag < 17.

and

b between -10. and 10.

and

phot_g_mean_mag - 1.75*bp_rp < 13.

and

parallax+parallax_error < power(10.,(10.-(phot_g_mean_mag - 1.75*bp_rp))/5.)

Rationale: 

-- vary by >0.32mag peak-to-peak

-- have a 'predicted' W1mag (== phot_g_mean_mag - 1.75*bp_rp) < 13.

-- have an W1 abs mag < 0: parallax+parallax_error < power(10.,(10.-(phot_g_mean_mag - 1.75*bp_rp))/5.)

That yields 27000 candidates, of which 6000 have good astrometry...

Of the 700 GaiaDR2 Cepheids, 95% get picked up that way; the rest is all typeII Cepheids.

The query output is named Cepheid_searches_GDR2only_v3-result.fits
and can be found here:
https://www.dropbox.com/s/7xwsnvruk8an58w/Cepheid_searches_GDR2only_v3-result.fits?dl=0

This is what the distribution looks like  [NB: we can do better with the X-axis by taking a spectroscopic-survey-trained estimate of Teff, derived from Gaia,2Mass & WISE photometry]

In this plot, I have used (J-K) - 0.25*(G-K) as a self-dereddened color; Ideally, I'd like to have Teff as the X-axis. YST to the rescue?

Now we need to look at the contamination by other types of variable stars (RV Tau, W Vir, RRL):

We do this by looking at "dereddened color" vs "abs. mag." (however lousy):

and compare this to the Cepheids from Gaia DR2 (in blue):

If we then plot the lump centered on (0.2,-5), 825 sources, they look like this

And the possible contaminant's sky distribution looks like this:

are these stars (at (0.1,0) in the color-absmag plane) where the instability strip crosses the main sequence? (Delta Scuti?)

Update January 25, 2019

I have done a broader candidate selection, Yuan-Sen Ting has then estimated their T_eff, as follows: we train a neural net on all APOGEE stars to predict T_eff(APOGEE) from BP,G,RP,J,H,K,W1,

and apply it to the candidates. Initial cross-validation indicates a precision of ~250-300K; in the range 4000K t o 8000K.

With this, one gets a candidate set that looks like this:

This shows the different classes of variables even more nicely: luminous red variables at 3500K, (presumed) RV Tau (at 4600K), and (presumed) RRL (& beta Ceph, whatever) at (6200K,0).

Comparison with the Gaia DR2 paper Cepheids (black) shows where the classical Cepheids should lie (and shows Gaia DR2's misclassification rate).

That suggest to select (in a more stringent fashion) like this

which leads to an on-sky distribution like that:

This sample selection includes (>90%) if the Gaia DR2 Cepheid I, and basically all Cepheid I selected by variability from WISE in a recent 2018 paper (incl de Grijs,  check reference).
It will be interesting to see what the stars near the GC (|l|<45) are.

Addendum (Feb 18, 2019)

HWR is discovering that there are analogous variability measures in BP and RP. Taking the 

"Cepheid candidate take 7" sample, it's fun to look at the distribution of the ratio of variability

in BP and RP. This should be followed-up.

Note that this is a funky X-axis -- the sqrt(phot_rp_n_obs) is missing. The unmarked stripe  at (0.015,1.5) are RV Tau (what the f...).